Mr. Boswell points out that most of them are relatively new immigrants, having come to the United States after 1959.

To many non-Hispanic residents in this area, Cuban-Americans in south Florida may appear to be stubbornly refusing to become part of the American scene. Their use of Spanish causes resentment among some who speak no Spanish.

But a visit to the Rivero family here provides a much different picture.

The five generations of Riveros here struggled hard to get to the US, and they have fully embraced the freedom and values of their new country, as well as many of its customs.

At a time when some community leaders contend that relations between Cuban-Americans and both blacks and whites are not at their best in this area, the younger Rivero family members say they have black and white friends.

Like many families of Cuban heritage in the US, the Riveros are hanging on to some of their dearest Cuban traditions.

They still have a family gathering and eat pork on Dec. 24. They eat exactly 12 grapes at the stroke of midnight on New Year's Eve, and they go all out to celebrate the 15th birthday (''Los Quinces'') of each girl in the family.

On Thanksgiving Day they serve black beans and rice along with the turkey.

But overall they are becoming very American, especially the younger members.

Maria says, for example, that she will not require her two-year-old daughter, Melissa, to have a chaperone when she is old enough to date. Cuban tradition calls for chaperones.

At the same time, she and her husband speak to Melissa only in Spanish. They want her to be bilingual, and they say she will get plenty of English once she goes to school.

Manuel Jr., Maria's brother, is a college graduate student and also works 20 to 35 hours a week for his father's construction company.

He says most Cubans his age mix Cuban and American cultures easily.

''Cubans like myself feel very comfortable having lunch at McDonald's but dinner at La Esquina de Tejas,'' he says.

''I don't mind listening to country music all day, then going home to listen to Channel 23'' (the Spanish-language station here).

During this writer's visit to the Rivero family here, Sylvia Cantillo, the 91 -year-old great, great grandmother of young Melissa, leans forward on the sofa and asks the correct way to pronounce ''hamburger.''

Mrs. Cantillo, who knows only a few words of English, was a primary school teacher for 42 years in Cuba. She came to the US in 1973. Altogether, 21 family members now live in this country, most of them within a few blocks of the spacious home of the Riveros.

Maria's grandfather, Servando Mosquera, who came here in 1967, speaks some English. ''I don't meet Americans,'' says the former Cuban TV and radio journalist.

Maria's father, who came here in 1962, is still most comfortable with Spanish. He was a bank official in Cuba.

He fought on Fidel Castro's side in the Cuban revolution but later became disenchanted with the regime. He says he'd like to retire to Cuba if they country ever gets rid of Castro and communism.

While a crowd of family members sat talking in the main living room and the kitchen, in another room Manuel Sr. and his wife Irma recalled the risk and hardships they went through to get to the US.

''When we came here it was very rough,'' says Mrs. Rivero, who speaks good English. ''We had to leave the whole family; everything we had.''

With the help of the underground in Cuba, Rivero obtained a 1961 Cuban passport. But the only US visa stamp obtained for him was for a year earlier. Even so, he risked apprehension and walked calmly with his wife through Cuban airport security to his new life of freedom.

''I was looking for liberty and a future, and to be able to express my opinion,'' he says.

He and his wife and son Manuel Jr. arrived here with only a single Cuban coin , which he has kept as a memento of the ordeal.

Manuel Sr. soon took a job as a dishwasher, walking five miles each way to the job. He progressed through a series of other jobs, often moonlighting on a second job. He now owns a small construction company which employs eight people.

Mrs. Rivero currently works as an attendance clerk at a local school.

''It used to be no self-respecting Cuban would allow his wife to work out of the family,'' says Boswell.

''Cubans are very work-oriented,'' he says, and in many families, both parents works.

But most Cubans in the US are far from wealthy. The Census Bureau in 1980 found that working Cubans in Florida had a median income of $6,175. About 75 percent of them earned less than $11,000 a year.

Cubans, says Manuel Jr., ''don't want to take over anything. They just want a piece of the pie.''